Finite Group Databasebeta

D42×C293 #34035806

order18752
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C293 · Schur multiplier (H2) = C26

Aliases

direct productD42×C293

Subgroups

subgroupG/H
center, socleC22×C293C24
commutator, Frattini, cosocleC22C24×C293
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C293 ◁ G

428 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4688

Conjugacy classes & character table

7325 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49157839, #49157901, #49157964, …
maximal subgroup of#1619×C293, #1629×C293, #1639×C293, …
maximal normal subgroup of#1619×C293, #1629×C293, #1639×C293, …
maximal quotient ofD4×C22⋊C4×C293, D4×C4⋊C4×C293, #2358×C293, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 226);